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# Simplify the expression $\frac{12x^3+13x^2-59x+30}{4x-5}$

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##  Final answer to the problem

$3x^2+7x-6$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Write in simplest form
• Solve by quadratic formula (general formula)
• Find the derivative using the definition
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

We can factor the polynomial $12x^3+13x^2-59x+30$ using the rational root theorem, which guarantees that for a polynomial of the form $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ there is a rational root of the form $\pm\frac{p}{q}$, where $p$ belongs to the divisors of the constant term $a_0$, and $q$ belongs to the divisors of the leading coefficient $a_n$. List all divisors $p$ of the constant term $a_0$, which equals $30$

$1, 2, 3, 5, 6, 10, 15, 30$

Learn how to solve polynomial long division problems step by step online.

$1, 2, 3, 5, 6, 10, 15, 30$

Learn how to solve polynomial long division problems step by step online. Simplify the expression (12x^3+13x^2-59x+30)/(4x-5). We can factor the polynomial 12x^3+13x^2-59x+30 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 30. Next, list all divisors of the leading coefficient a_n, which equals 12. The possible roots \pm\frac{p}{q} of the polynomial 12x^3+13x^2-59x+30 will then be. Trying all possible roots, we found that \frac{5}{4} is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

##  Final answer to the problem

$3x^2+7x-6$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
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y
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(◻)
+
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×
◻/◻
/
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2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.